What is the value of cos((17pi)/8) ?

The value of cos((17pi)/8) is (sqrt(2+\sqrt{2)})/2

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cos((17pi)/8)

cos (\frac{17 π}{8})

\frac{2 + 2}{2}

Solution steps

cos (\frac{17 π}{8})

cos (\frac{17 π}{8}) = cos (\frac{π}{8})

= cos (\frac{π}{8})

Rewrite using trig identities:

\frac{1 + cos ( \frac{π}{4} )}{2}

= \frac{1 + cos ( \frac{π}{4} )}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

= \frac{1 + \frac{2}{2}}{2}

Simplify

\frac{1 + \frac{2}{2}}{2} : \frac{2 + 2}{2}

= \frac{2 + 2}{2}

sin (10 1^{\circ})

cos (10 5^{\circ}) cos (1 5^{\circ})

cos (2 (\frac{π}{8}))

4 (cos (3 0^{\circ}))

- 7 sin (- \frac{π}{6})

What is the value of cos((17pi)/8) ?
The value of cos((17pi)/8) is (sqrt(2+\sqrt{2)})/2